An open glass tube is immersed in mercury in such a way that a length of 8 cm extends above the mercury level. The open end of the tube is then closed and sealed and the tube is raised vertically up by additional 46 cm. what will be length of the air column above mercury in the above now ?
(Atmospheric pressure = 76 cm of Hg)

Options

A. 38 cm
B. 6 cm
C. 16 cm
D. 22 cm

Answer

C

Explanation

Let area of tube is A
This phenomenon occurs at constant temperature, i.e, isothermal process. When tube is open, pressure is `P_(a)` in tube at mercury level and after closing the tube, pressure inside the tube at mercury level is P..
At constant temperature `P_(1)V_(1)=P_(2)V_(2)`
`P_(a) (A)(8)=P(A) (54-x)`
`P_(a)` =76 cm of mercury column
P.=(76-x) cm of mercury column, as the pressure decreases with depth.
`76(A) (8)=(76-x)A (54-x)`
`608=76 xx 54 -76x-54x+x^(2)`
`or x^(2)-130x+3496=0`
Solving we get, x=38 or x=92
As `x lt 54`
x=38
Height of air column above merucry level =54-38 =16cm